Related papers: Algorithms for tensor network renormalization

With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…

Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…

Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

Tensor networks representations of many-body quantum systems can be described in terms of quantum channels. We focus on channels associated with the Multi-scale Entanglement Renormalization Ansatz (MERA) tensor network that has been…

We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th…

In this paper, a way of generalizing the tensor renormalization group(TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is…

This paper presents a dynamic network rewiring (DNR) method to generate pruned deep neural network (DNN) models that are robust against adversarial attacks yet maintain high accuracy on clean images. In particular, the disclosed DNR method…

Recurrent neural networks (RNNs), originally developed for natural language processing, hold great promise for accurately describing strongly correlated quantum many-body systems. Here, we employ 2D RNNs to investigate two prototypical…

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…

The computation and storage requirements for Deep Neural Networks (DNNs) are usually high. This issue limits their deployability on ubiquitous computing devices such as smart phones, wearables and autonomous drones. In this paper, we…

Tensor network (TN) states, including entanglement renormalization (ER), can encompass a wider variety of entangled states. When the entanglement structure of the quantum state of interest is non-uniform in real space, accurately…

The quantum state preparation of probability distributions is an important subroutine for many quantum algorithms. When embedding $D$-dimensional multivariate probability distributions by discretizing each dimension into $2^n$ points, we…

We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently…

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…

We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…